This invention relates to tessellatable elements and to plane tessellations made from such elements. The tessellatable elements may be paving stones or blocks, bricks, tiles, decorative covering elements, playing cards, game pieces, etc., and the tessellations may form coverings and pavings of various kinds for various purposes including pedestrian walks, driveways, streets, floors, walls, decorations, games, puzzles, mazes, mosaics, patterns on fabrics and within computer software games, computer simulation, computer displays, etc.
It is usual to cover or decorate surfaces such as walls and floors with elements such as bricks, paving stones and tiles. For aesthetic reasons, and for uniformity, surface coverings and decorations often comprise a tessellation of elements. A tessellation is an arrangement of polygons without gaps or overlapping, usually in a repeated pattern. For example, in pedestrian malls and crossings it is common to have walkways made of a repeated pattern of rectangular paving stones. A `herring-bone` pattern made of identically-sized rectangular paving stones is popular for this purpose.
In practice, it is usually sufficient with paving stones for example to combine shapes that approximately tessellate, since any gaps may be filled by, e.g., mortar or sand.
Sometimes surface coverings and decorations have mosaics incorporated therein. To form a picture or pattern from a mosaic of rectangular elements often involves the reshaping of elements by cutting, particularly if the picture or pattern includes curves or bends. It will be appreciated that the cutting of paving stones, for example, is both physically strenuous and time consuming and can involve considerable wastage of material.
It is also well known to use tessellations for patterns in children's' coloring books and for jig-saw and puzzle games.